The rectifiability of singular sets for geometric flows (I)--Yang-Mills flow
Jian Zhai
TL;DR
This paper proves that certain monotonicity and energy conditions ensure the singular sets in Yang-Mills flow are rectifiable, advancing understanding of the geometric structure of singularities.
Contribution
It establishes the rectifiability of singular sets in Yang-Mills flow under specific monotonicity and energy inequalities, a novel result in geometric analysis.
Findings
Singular sets are rectifiable under given conditions
Monotonicity of density is crucial for rectifiability
Energy inequalities imply geometric regularity
Abstract
We prove that monotonicity of density and energy inequality imply the rectifiability of the singular sets for Yang-Mills flow.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Point processes and geometric inequalities